tan(45° + θ) · tan(45° − θ) is equal to:
A(1 + tan²θ) / (1 − tan²θ)
B(1 − tan θ) / (1 + tan θ)
Ctan 2θ
D1
Answer & Solution
Correct answer: D. 1
1. tan(45° + θ) = (1 + tan θ) / (1 − tan θ); tan(45° − θ) = (1 − tan θ) / (1 + tan θ).
2. Multiplying them: [(1+tanθ)/(1−tanθ)] · [(1−tanθ)/(1+tanθ)] = 1.
3. So the product equals 1 for any θ where both tans are defined.
_Source: NCERT Class 11 Maths Ch 3 §3.4 Trig Identities_
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